Nuprl Lemma : ranked-eo-before
∀[L:Id ⟶ (Top List)]. ∀[rk:Top]. ∀[e:E]. (before(e) ~ map(λn.<fst(e), n>;upto(snd(e))))
Proof
Definitions occuring in Statement :
ranked-eo: ranked-eo(L;rk),
es-before: before(e),
es-E: E,
Id: Id,
upto: upto(n),
map: map(f;as),
list: T List,
uall: ∀[x:A]. B[x],
top: Top,
pi1: fst(t),
pi2: snd(t),
lambda: λx.A[x],
function: x:A ⟶ B[x],
pair: <a, b>,
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
top: Top,
pi1: fst(t),
pi2: snd(t),
subtype_rel: A ⊆r B,
uimplies: b supposing a,
le: A ≤ B,
and: P ∧ Q,
less_than': less_than'(a;b),
false: False,
not: ¬A,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
nat: ℕ,
ge: i ≥ j ,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
guard: {T},
int_seg: {i..j-},
lelt: i ≤ j < k,
decidable: Dec(P),
or: P ∨ Q,
less_than: a < b,
so_lambda: λ2x.t[x],
so_apply: x[s],
es-before: before(e),
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
ifthenelse: if b then t else f fi ,
bfalse: ff,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
nequal: a ≠ b ∈ T ,
int_upper: {i...},
Id: Id,
nil: [],
map: map(f;as),
list_ind: list_ind,
upto: upto(n),
from-upto: [n, m),
lt_int: i <z j,
nat_plus: ℕ+,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
true: True
Latex:
\mforall{}[L:Id {}\mrightarrow{} (Top List)]. \mforall{}[rk:Top]. \mforall{}[e:E]. (before(e) \msim{} map(\mlambda{}n.<fst(e), n>upto(snd(e))))
Date html generated:
2016_05_17-AM-08_44_57
Last ObjectModification:
2016_01_17-PM-02_42_20
Theory : event-ordering
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